Question

What is the value of x in the equation 1/5 x-2/3 y=30 when y =15

Answer 1

The answer:  x = 200 .
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Explanation:
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Given the equation:
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(1/5)x  -  (2/3)y = 30 ; 

What is the value of "x" when "y" = 15 ?
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Plug in "15" for "y" into the equation; and solve:

(1/5)x  -  (2/3)*15 = 30 ;

Note:  $\frac{2}{3}*( \frac{15}{1}) = \frac{2*15}{3*1} = \frac{30}{3} = 10 ;$


OR: $\frac{2}{3} * \frac{15}{1} = ? ;\\The "3" cancels out to a "1" ; and the "15" cancels out and is replaced with a "5" ; since; "(15÷3=5") ; and since: "(3÷3=1)" ; and we have:\\[tex] \frac{2}{1} * \frac{5}{1} = \frac{2*5}{1*1} = \frac{10}{1} = 10 ;$

Or:  [tex] \frac{2}{1} * \frac{5}{1} = 2 * 5 ; (since 2/1 = 2;  and since 5/1 = 6 ;

                                                    → 2 * 5 = 10 ;
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So, we can rewrite the equation:  
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(1/5)x  -  (2/3)y = 30 ;  and replace "(2/3)y"  with "10") ;

(1/5)x  -  10 = 30 ;  

Add "10" to EACH SIDE of the equation;

               (1/5)x  -  10 + 10 = 30 + 10 ; 

to get:   (1/5)x  = 40 ; 

Now, multiply EACH SIDE of the equation by "5" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
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                 5* (1/5)x = 40 * 5 ;
 
                             x = 200 ;
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The answer:  x = 200 .
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Answer 2

First replace y with 15.
1/5x-10=30
Then just solve from there.
x=200